[" If "ax^(2)+bx+c=0" and "bx^(2)+cx+a=0" have a "],[" common root and "a!=0" then "(a^(3)+b^(3)+c^(3))/(abc)" is "]

If ax^(2)+bx+c=0 and bx^(2)+cx+a=0 have a common root, prove that a+b+c=0 or a=b=c .

Suppose the that quadratic equations ax^(2)+bx+c=0 and bx^(2)+cx+a=0 have a common root. Then show that a^(3)+b^(3)+c^(3)=3abc .

Suppose the that quadratic equations ax^(2)+bx+c=0 and bx^(2)+cx+a=0 have a common root. Then show that a^(3)+b^(3)+c^(3)=3abc .

If ax^(2)+bx+c=0andbx^(2)+cx+a=0 have a common root then the relation between a,b,c is

If ax^(2) + 2bx + c = 0 and ax^(2) + 2cx + b = 0, b ne c have a common root, then (a + b + c)/( a) is equal to

If x^(2)+bx+c=0,x^(2)+cx+b=0(b!=c) have a common root then b+c=

If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c

If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c

If one root of the equations ax^(2)+bx+c=0 and bx^(2)+cx+a=0, (a, b, c in R) is common, then the value of ((a^(3)+b^(3)+c^(3))/(abc))^(3) is